Question

How do you divide `\frac { 21h ^ { 2} - 24h + 3} { 2h - 5} \div \frac { 7h ^ { 2} - 8h + 1} { 2h - 5}`?

Answer 1

`(21h^2-24h+3)/(2h+5)-:(7h^2 - 8h + 1)/(2h-5) = color(blue)(3`

Explanation:

Dividing two terms with the same denominator cancels the denominators:

`(21h^2-24h+3)/(2h+5)-:(7h^2 - 8h + 1)/(2h-5)`

`= (21h^2-24h+3)/(cancel(2h+5))xx(cancel(2h-5))/(7h^2 - 8h + 1)`

`= (21h^2-24h+3)/(7h^2-8h+1)`

We can actually visibly see this answer is `3`, because multiplying all terms in the denominator by `3` yields the numerator, so

`(21h^2-24h+3)/(2h+5)-:(7h^2 - 8h + 1)/(2h-5) = color(blue)(ul(3`